In number classification using neural network, is training with edge image better than gray image?
Theoretically you will have no gain in the error ratio if the system preprocess the images with a linear high-pass filter before to send the image to the NN. 

Let see a simple 1-dimension case that supports this statement:

Assume inputs are "a", "b" and "c". A node at first hidden layer will receive an input to the activation function equal to s=w1*a+w2*b*w3*c+... being w1, w2, w3, ... the weights for this node.

Now, assume a simple differential case, where inputs will be ... , b'=b-a, c'=c-b, ... being the input to the hidden node s=w1'a'+w2'b'+w3'c'+...=...+w2'(b-a)+w3'(c-b)+...=...+(w2'-w3')b+...

Note both inputs to hidden node are the same if w1=w1'-w2', w2=w2'-w3', ... . So, the NN can itself perform the equivalent of the linear high-pass filtering adjusting the weights of the first hidden layer.

However, changes in learning speed (convergence time) can be expected.

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